Reversible maps in isometry groups of spherical, Euclidean and hyperbolic space

Short, Ian (2008). Reversible maps in isometry groups of spherical, Euclidean and hyperbolic space. Mathematical Proceedings of the Royal Irish Academy, 108A(1) pp. 33–46.

DOI: https://doi.org/10.3318/PRIA.2008.108.1.33

Abstract

An element of a group is reversible if it is conjugate to its own inverse, and it is strongly reversible if it is conjugate to its inverse by an involution. A group element is strongly reversible if and only if it can be expressed as a composite of two involutions. In this paper the reversible maps, the strongly reversible maps and those maps that are expressible as a composite of three involutions are determined in the isometry groups of spherical, Euclidean and hyperbolic space in several dimensions.

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